Optimized aerodynamic profile for a turbine vane, in particular for a nozzle of the second stage of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Z′ given in Table 1, in which the coordinate Z′ is the quotient D/H where D is the distance of the point under consideration from a first reference plane P 0  situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P 1 . The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

The present invention relates to an aerodynamic profile for a turbine vane.

In particular, the invention relates to the aerodynamic profile of a nozzle vane forming a portion of the stator of a gas turbine, and more particularly of a low pressure turbine of the type used in a turbojet of an aircraft.

The invention relates in particular to a nozzle vane of the second stage of a turbine having a plurality of stages, preferably four stages.

Such a profile should enable the turbine to provide the desired efficiency, and in order to do that it must be such that the flow of air around the profile is sound, i.e. substantially such that it does not give rise to turbulence, which is harmful for overall efficiency.

It must be capable of being installed properly in the environment of the engine, and in particular, for a nozzle vane forming a portion of the stator of the turbine, it must be capable of being fastened easily to the sectors of the foot platform (the zone of the vane that is furthest from the axis of rotation of the turbine) and of the head platform (the zone that is closest to said axis). Furthermore, this part must be capable of being obtained by casting, and must therefore present a profile that is compatible with that manufacturing technique.

Furthermore, the profile of the vane must enable it to withstand the mechanical stresses to which the vane is subjected, by enabling those stresses to be spread over the entire vane in such a manner as to avoid premature wear thereof. This spreading must apply both in static mode and in dynamic mode.

An object of the invention is to propose an aerodynamic profile for a turbine vane that is optimized, and capable of satisfying those objectives.

This object is achieved by the fact that when cold and in a non-coated state, said profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Z′ given in Table 1, in which the coordinate Z′ is the quotient D/H where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane that is the intersection of the stacking axis of the set of vanes and the axisymmetric surface of the hub, out to a second reference plane that is the intersection of said stacking axis with the axisymmetric surface of the casing, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.

This profile has been determined as a result of numerous tests and simulations. It is defined cold, i.e. at an ambient temperature of 20° C. That is a reference temperature at which the profile is geometrically determined. The above-mentioned objectives of aerodynamics and mechanical optimization are naturally valid for the conditions of use of this aerodynamic profile, i.e. when hot, at a temperature that is stabilized when the engine of which the turbine forms a part is being used under cruising conditions.

Furthermore, the aerodynamic profile of the invention is defined in the non-coated state. Since turbine vanes are subjected to high temperature gradients, it is common practice for them to be provided with a coating having thermal properties enabling them more easily to withstand such temperature variations. The profile is determined prior to installing such a coating.

It is stated above that the profile of the invention is “substantially identical” to the nominal profile. This means that the profile may depart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of ±1 millimeter (mm) in a direction normal to the surface of the nominal profile.

This variation takes account in particular of manufacturing tolerances of the profile.

It is also preferable for the X,Y coordinates of the aerodynamic profile to lie within a range of ±5% relative to the X,Y coordinates of the nominal profile.

This variation takes account of the setting of the profile to adapt to the flow coming from the blades of the turbine situated upstream, so as to further improve the efficiency of the turbine. In particular, the profile is adapted so as to be optimized for the flow coming from the rotary wheel of the first stage of a turbine when the vane of the invention belongs to the nozzle of the second stage of a turbine.

With a nozzle vane, i.e. a portion of the stator of a turbine, the profile serves to orient the fluid correctly for the turbine blades that are situated downstream, and that belong in particular to the rotary wheel of the second stage of the turbine.

The invention can be better understood and its advantages appear better on reading the following detailed description of an embodiment given by way of non-limiting example. The description refers to the accompanying drawings, in which:

FIG. 1 is a fragmentary axial section view of a turbine including a vane of profile that corresponds to that of the invention;

FIG. 2 is a perspective view of a vane to which the invention applies; and

FIG. 3 is a diagrammatic section view of the FIG. 2 vane on an X-Y plane.

The turbine shown in axial section in FIG. 1 comprises four stages referenced respectively E1 to E4. In the direction S going from upstream to downstream, each stage comprises a nozzle that forms a portion of the stator of the turbine and that has a plurality of radially-oriented vanes, and a rotary wheel that forms a portion of the rotor of the turbine and that likewise includes a plurality of radially-oriented blades.

In FIG. 1, the vanes of the nozzles of stages E1 to E4 are given references D1 to D4, whereas the blades of rotary wheels of stages E1 to E4 are given respective references R1 to R4.

In known manner, the vanes of the nozzles are fastened at both ends to stationary structure portions, while the blades of the rotary wheels are fastened to a rotary disk via their roots that are formed at their radially-inner ends closer to the axis of the rotation A of the turbine. The disks d1 to d4 forming parts of the wheels R1 to R4 are constrained to rotate together.

The invention relates in particular to a vane D2 which is a vane of the nozzle of the second stage E2 of the turbine that, as mentioned above, preferably comprises four stages, without this number being limiting.

Via its foot 10, which is its end remote from the axis of rotation A (see FIG. 1), the vane is fastened to the outer ring 12 of the turbine, which ring is stationary in rotation. Via its head 14, formed by its end closer to the axis of rotation A, the vane is fastened to an inner shroud 16 of the turbine. By convention, the aerodynamic profile 18 of the vane is the entire portion of said vane that extends radially outwards from its head 14 to its foot 10 without incorporating the fastenings respectively to the outer ring 12 and to the inner shroud 16.

In FIG. 2, there can be seen a frame of reference comprising Cartesian coordinates X,Y,Z. The radial direction Z is the height direction of the vane, which extends radially from its head to its foot. This direction Z is perpendicular to the axial direction X which is the direction of the axis of rotation A of the turbine. The direction Y is perpendicular to the X,Z plane and is therefore tangential to the direction of rotation of the turbine.

The nominal profile from which the aerodynamic profile of the invention is determined is defined in following Table 1 of coordinates, in which the coordinates Z′, measured along the axis Z is non-dimensional, whereas the dimensions X and Y, respectively measured along the axes X and Y, are expressed in millimeters.

TABLE 1 X Y Z′ X Y Z′ X Y Z′ −20.0412 7.84905 −0.09 2.93829 10.6902 0.6 2.10808 12.9994 0.95 −20.0606 7.79348 −0.09 3.41716 11.7351 0.6 1.37972 12.109 0.95 −20.0776 7.70968 −0.09 3.85481 12.721 0.6 0.58084 11.2153 0.95 −20.0834 7.57783 −0.09 4.25382 13.6416 0.6 −0.29352 10.335 0.95 −20.0575 7.39578 −0.09 4.61658 14.4918 0.6 −1.25082 9.49068 0.95 −19.975 7.17023 −0.09 4.94462 15.2677 0.6 −2.29723 8.71052 0.95 −19.8321 6.9067 −0.09 5.23872 15.9667 0.6 −3.431 8.02097 0.95 −19.6276 6.60812 −0.09 5.49938 16.5874 0.6 −4.64475 7.44967 0.95 −19.3599 6.27744 −0.09 5.72712 17.1296 0.6 −5.92293 7.01949 0.95 −19.0326 5.91317 −0.09 5.92264 17.5939 0.6 −7.24378 6.74865 0.95 −18.6482 5.51443 −0.09 6.08754 17.982 0.6 −8.58001 6.64057 0.95 −18.2036 5.08653 −0.09 6.21961 18.2986 0.6 −9.90461 6.68895 0.95 −17.6959 4.636 −0.09 6.32913 18.5442 0.6 −11.1926 6.88679 0.95 −17.1245 4.16871 −0.09 6.38178 18.7381 0.6 −12.4274 7.19905 0.95 −16.4849 3.69689 −0.09 6.35414 18.8756 0.6 −13.5978 7.60088 0.95 −15.7742 3.23423 −0.09 6.29978 18.9454 0.6 −14.6849 8.09597 0.95 −14.993 2.79249 −0.09 6.24421 18.9845 0.6 −15.6971 8.63249 0.95 −14.1412 2.38943 −0.09 6.19314 19.0053 0.6 −16.6598 9.14563 0.95 −13.2225 2.04047 −0.09 6.12207 19.0153 0.6 −17.5745 9.62094 0.95 −12.2437 1.76111 −0.09 6.0119 18.9869 0.6 −18.4496 10.0305 0.95 −11.2134 1.57023 −0.09 5.89089 18.8777 0.6 −19.2933 10.336 0.95 −10.1445 1.48866 −0.09 5.77575 18.6924 0.6 −20.1014 10.503 0.95 −9.05516 1.53566 −0.09 5.63348 18.4532 0.6 −20.8514 10.5163 0.95 −7.96862 1.72449 −0.09 5.45739 18.1598 0.6 −21.5122 10.3873 0.95 −6.91074 2.05792 −0.09 5.24698 17.8093 0.6 −22.061 10.1566 0.95 −5.90384 2.52372 −0.09 5.00151 17.4002 0.6 −22.4955 9.87622 0.95 −4.96185 3.0986 −0.09 4.72014 16.9319 0.6 −22.827 9.58698 0.95 −4.09003 3.75553 −0.09 4.40242 16.405 0.6 −23.0701 9.31545 0.95 −3.28794 4.46935 −0.09 4.04785 15.8206 0.6 −23.241 9.07878 0.95 −2.55433 5.22059 −0.09 3.65592 15.1812 0.6 −23.3568 8.88762 0.95 −1.87968 5.98657 −0.09 3.226 14.4898 0.6 −23.432 8.74586 0.95 −1.25825 6.75216 −0.09 2.7573 13.7507 0.6 −23.477 8.65219 0.95 −0.68722 7.50681 −0.09 2.24829 12.9692 0.6 −23.5064 8.58696 0.95 −0.15958 8.2383 −0.09 1.69694 12.152 0.6 −24.1523 8.75918 0.975 0.32858 8.93811 −0.09 1.10199 11.3058 0.6 −24.187 8.67585 0.975 0.778 9.60077 −0.09 0.46021 10.4399 0.6 −24.2328 8.5529 0.975 1.19172 10.2201 −0.09 −0.23145 9.56443 0.6 −24.2931 8.3596 0.975 1.57099 10.7919 −0.09 −0.97594 8.69092 0.6 −24.3562 8.08463 0.975 1.91563 11.3137 −0.09 −1.77628 7.83251 0.6 −24.401 7.71891 0.975 2.22577 11.7835 −0.09 −2.63531 7.00439 0.6 −24.388 7.25913 0.975 2.50168 12.2002 −0.09 −3.55355 6.22217 0.6 −24.2665 6.7174 0.975 2.7434 12.5637 −0.09 −4.52958 5.50253 0.6 −24.0346 6.10723 0.975 2.95118 12.8746 −0.09 −5.56002 4.86371 0.6 −23.6866 5.44134 0.975 3.12503 13.135 −0.09 −6.63718 4.32259 0.6 −23.2115 4.73684 0.975 3.26947 13.3447 −0.09 −7.74884 3.89279 0.6 −22.612 4.00412 0.975 3.37493 13.5142 −0.09 −8.87928 3.58443 0.6 −21.8869 3.2566 0.975 3.40963 13.6592 −0.09 −10.0102 3.40394 0.6 −21.0301 2.51596 0.975 3.38417 13.7601 −0.09 −11.1217 3.35203 0.6 −20.0387 1.80593 0.975 3.34717 13.8144 −0.09 −12.1935 3.42178 0.6 −18.9174 1.14607 0.975 3.31045 13.849 −0.09 −13.2085 3.59774 0.6 −17.6722 0.55869 0.975 3.27564 13.8724 −0.09 −14.1546 3.85682 0.6 −16.3126 0.06675 0.975 3.22577 13.8946 −0.09 −15.0256 4.17391 0.6 −14.856 −0.32245 0.975 3.13999 13.9063 −0.09 −15.8197 4.52625 0.6 −13.3203 −0.60649 0.975 3.02203 13.868 −0.09 −16.5371 4.89549 0.6 −11.7216 −0.77464 0.975 2.89458 13.7617 −0.09 −17.1786 5.26829 0.6 −10.0771 −0.80038 0.975 2.75211 13.605 −0.09 −17.7448 5.6348 0.6 −8.41149 −0.6446 0.975 2.5767 13.4127 −0.09 −18.2379 5.98606 0.6 −6.76219 −0.26692 0.975 2.37112 13.1793 −0.09 −18.6633 6.31088 0.6 −5.17669 0.35122 0.975 2.12787 12.9099 −0.09 −19.0326 6.59359 0.6 −3.69424 1.18759 0.975 1.84809 12.6026 −0.09 −19.354 6.82412 0.6 −2.34294 2.20768 0.975 1.53099 12.2582 −0.09 −19.6297 7.00119 0.6 −1.13402 3.36677 0.975 1.17645 11.8778 −0.09 −19.8702 7.10658 0.6 −0.05964 4.61555 0.975 0.78286 11.4646 −0.09 −20.0695 7.13263 0.6 0.8881 5.91824 0.975 0.34838 11.0232 −0.09 −20.2111 7.10529 0.6 1.72438 7.24227 0.975 −0.12826 10.5583 −0.09 −20.2958 7.06585 0.6 2.46652 8.56057 0.975 −0.6487 10.076 −0.09 −20.3488 7.02937 0.6 3.12995 9.85204 0.975 −1.21552 9.5848 −0.09 −20.5367 7.15017 0.7 3.72492 11.1014 0.975 −1.83003 9.09318 −0.09 −20.5884 7.0882 0.7 4.25978 12.2962 0.975 −2.49319 8.61088 −0.09 −20.6412 6.98341 0.7 4.74322 13.4255 0.975 −3.20534 8.14901 −0.09 −20.6695 6.80459 0.7 5.18032 14.4814 0.975 −3.96501 7.7185 −0.09 −20.6332 6.55496 0.7 5.57451 15.4575 0.975 −4.76836 7.32877 −0.09 −20.5263 6.24332 0.7 5.92865 16.3491 0.975 −5.60979 6.98809 −0.09 −20.3691 5.86327 0.7 6.24489 17.1528 0.975 −6.48214 6.70317 −0.09 −20.1515 5.41706 0.7 6.52464 17.8667 0.975 −7.37622 6.47563 −0.09 −19.871 4.90525 0.7 6.76912 18.4902 0.975 −8.28247 6.30393 −0.09 −19.5261 4.32871 0.7 6.97911 19.0242 0.975 −9.19179 6.18479 −0.09 −19.1078 3.69445 0.7 7.15609 19.4707 0.975 −10.0958 6.11413 −0.09 −18.6044 3.01383 0.7 7.29827 19.8345 0.975 −10.9869 6.08822 −0.09 −18.0063 2.30022 0.7 7.41596 20.1173 0.975 −11.858 6.10366 −0.09 −17.3056 1.56913 0.7 7.48672 20.3349 0.975 −12.7028 6.15696 −0.09 −16.4953 0.83957 0.7 7.47028 20.4938 0.975 −13.5152 6.24594 −0.09 −15.5696 0.13487 0.7 7.41232 20.5762 0.975 −14.2883 6.37437 −0.09 −14.5249 −0.51639 0.7 7.34898 20.6206 0.975 −15.0167 6.53642 −0.09 −13.3604 −1.07785 0.7 7.29081 20.6418 0.975 −15.6954 6.72793 −0.09 −12.0815 −1.50427 0.7 7.21044 20.6475 0.975 −16.3187 6.9479 −0.09 −10.7059 −1.74451 0.7 7.09176 20.6004 0.975 −16.8895 7.17381 −0.09 −9.26855 −1.75243 0.7 6.97216 20.462 0.975 −17.4095 7.39339 −0.09 −7.81918 −1.50352 0.7 6.84947 20.25 0.975 −17.8795 7.59925 −0.09 −6.4087 −1.00545 0.7 6.69417 19.9789 0.975 −18.3024 7.78166 −0.09 −5.07482 −0.29157 0.7 6.50225 19.6462 0.975 −18.683 7.92678 −0.09 −3.83778 0.59445 0.7 6.26936 19.2508 0.975 −19.0212 8.03038 −0.09 −2.70661 1.61267 0.7 5.99373 18.7917 0.975 −19.3155 8.0934 −0.09 −1.67932 2.72467 0.7 5.67455 18.2681 0.975 −19.5637 8.11687 −0.09 −0.74641 3.8961 0.7 5.31213 17.6801 0.975 −19.7619 8.09235 −0.09 0.09817 5.10289 0.7 4.90449 17.0302 0.975 −19.9003 8.02726 −0.09 0.86166 6.32436 0.7 4.44745 16.3232 0.975 −19.9803 7.95211 −0.09 1.55466 7.54111 0.7 3.93713 15.5651 0.975 −20.0199 7.8931 −0.09 2.18564 8.73764 0.7 3.36906 14.7636 0.975 −20.0412 7.84905 −0.09 2.76008 9.90186 0.7 2.73926 13.9274 0.975 −20.0156 7.71856 −0.044 3.28336 11.0231 0.7 2.0443 13.0662 0.975 −20.0414 7.66381 −0.044 3.7618 12.0913 0.7 1.27969 12.1925 0.975 −20.0662 7.57942 −0.044 4.19839 13.0993 0.7 0.44212 11.3195 0.975 −20.0782 7.4442 −0.044 4.59597 14.0405 0.7 −0.47255 10.464 0.975 −20.0515 7.25696 −0.044 4.95709 14.9098 0.7 −1.47218 9.65137 0.975 −19.9658 7.02527 −0.044 5.28338 15.7031 0.7 −2.5611 8.90991 0.975 −19.8207 6.75318 −0.044 5.57577 16.4179 0.7 −3.73779 8.27023 0.975 −19.618 6.44103 −0.044 5.83488 17.0527 0.7 −4.99426 7.76574 0.975 −19.3545 6.09166 −0.044 6.06125 17.607 0.7 −6.31326 7.42945 0.975 −19.0306 5.70588 −0.044 6.25563 18.0818 0.7 −7.66508 7.27274 0.975 −18.6483 5.28361 −0.044 6.41952 18.4788 0.7 −9.01796 7.29569 0.975 −18.2048 4.82953 −0.044 6.55055 18.8026 0.7 −10.3394 7.5041 0.975 −17.6966 4.35092 −0.044 6.66047 19.0534 0.7 −11.6134 7.83114 0.975 −17.1211 3.85563 −0.044 6.71513 19.2505 0.7 −12.8425 8.20786 0.975 −16.4744 3.35555 −0.044 6.68665 19.3905 0.7 −14.0196 8.62525 0.975 −15.7533 2.86484 −0.044 6.63108 19.4614 0.7 −15.1404 9.06962 0.975 −14.9569 2.39825 −0.044 6.57427 19.5009 0.7 −16.2046 9.5218 0.975 −14.085 1.97471 −0.044 6.52255 19.5215 0.7 −17.2144 9.96052 0.975 −13.141 1.6134 −0.044 6.45071 19.5309 0.7 −18.1723 10.3668 0.975 −12.1319 1.3344 −0.044 6.33981 19.501 0.7 −19.09 10.6965 0.975 −11.0685 1.15968 −0.044 6.21933 19.389 0.7 −19.9717 10.9039 0.975 −9.96697 1.11074 −0.044 6.10592 19.2001 0.7 −20.8023 10.9632 0.975 −8.84938 1.20451 −0.044 5.96375 18.9578 0.7 −21.5544 10.8761 0.975 −7.74176 1.44911 −0.044 5.78882 18.6599 0.7 −22.2018 10.6696 0.975 −6.67046 1.84136 −0.044 5.57896 18.3046 0.7 −22.7335 10.3897 0.975 −5.65661 2.36499 −0.044 5.33356 17.8902 0.7 −23.1546 10.0813 0.975 −4.71198 2.99431 −0.044 5.05198 17.416 0.7 −23.4782 9.77732 0.975 −3.83971 3.70127 −0.044 4.73357 16.8827 0.7 −23.7176 9.49806 0.975 −3.03857 4.46141 −0.044 4.3778 16.2915 0.7 −23.8872 9.25708 0.975 −2.30594 5.25491 −0.044 3.98393 15.6449 0.7 −24.0028 9.06331 0.975 −1.63266 6.06045 −0.044 3.55115 14.9462 0.7 −24.0779 8.91986 0.975 −1.0127 6.86312 −0.044 3.07851 14.1997 0.7 −24.123 8.82514 0.975 −0.44276 7.65217 −0.044 2.56445 13.411 0.7 −24.1523 8.75918 0.975 0.08342 8.41619 −0.044 2.00704 12.5865 0.7 −24.7404 8.88186 1 0.56997 9.14657 −0.044 1.40402 11.734 0.7 −24.7763 8.79786 1 1.01806 9.83754 −0.044 0.75338 10.8619 0.7 −24.8231 8.67359 1 1.43024 10.4833 −0.044 0.0513 9.98122 0.7 −24.8825 8.47746 1 1.80776 11.0796 −0.044 −0.70586 9.10423 0.7 −24.9392 8.19759 1 2.15079 11.6236 −0.044 −1.52095 8.24438 0.7 −24.967 7.8257 1 2.45947 12.1135 −0.044 −2.39705 7.41774 0.7 −24.9292 7.3617 1 2.73398 12.5481 −0.044 −3.33466 6.64078 0.7 −24.7874 6.81795 1 2.9744 12.9273 −0.044 −4.33172 5.93054 0.7 −24.5402 6.20531 1 3.18102 13.2517 −0.044 −5.38405 5.3056 0.7 −24.1806 5.53525 1 3.35404 13.5233 −0.044 −6.48281 4.7826 0.7 −23.6999 4.8221 1 3.49747 13.7424 −0.044 −7.61438 4.37374 0.7 −23.1004 4.07458 1 3.60298 13.9186 −0.044 −8.76187 4.08661 0.7 −22.377 3.30802 1 3.6388 14.0677 −0.044 −9.90663 3.92481 0.7 −21.5204 2.54631 1 3.61321 14.1717 −0.044 −11.0292 3.88599 0.7 −20.5263 1.81493 1 3.57466 14.2271 −0.044 −12.1109 3.96087 0.7 −19.3971 1.13746 1 3.53626 14.262 −0.044 −13.1363 4.13372 0.7 −18.1387 0.53881 1 3.50001 14.2851 −0.044 −14.0946 4.38297 0.7 −16.7616 0.0438 1 3.44819 14.3063 −0.044 −14.9802 4.68528 0.7 −15.2834 −0.33509 1 3.35983 14.3141 −0.044 −15.791 5.01953 0.7 −13.7241 −0.59413 1 3.24112 14.2688 −0.044 −16.527 5.36855 0.7 −12.103 −0.73266 1 3.11479 14.1549 −0.044 −17.1889 5.719 0.7 −10.4385 −0.74331 1 2.97305 13.9906 −0.044 −17.7784 6.05989 0.7 −8.75185 −0.59397 1 2.79765 13.7896 −0.044 −18.2978 6.38178 0.7 −7.07341 −0.25414 1 2.592 13.5461 −0.044 −18.7535 6.67223 0.7 −5.45367 0.33143 1 2.34963 13.2639 −0.044 −19.1545 6.91637 0.7 −3.94774 1.16809 1 2.07093 12.9419 −0.044 −19.5064 7.10513 0.7 −2.56462 2.17979 1 1.75522 12.5807 −0.044 −19.81 7.23639 0.7 −1.31631 3.32657 1 1.40243 12.1813 −0.044 −20.0676 7.29845 0.7 −0.202 4.56682 1 1.01115 11.7468 −0.044 −20.2704 7.29079 0.7 0.78657 5.86345 1 0.57968 11.2813 −0.044 −20.408 7.24316 0.7 1.65923 7.18659 1 0.10679 10.7894 −0.044 −20.4879 7.19297 0.7 2.43148 8.50876 1 −0.40917 10.277 −0.044 −20.5367 7.15017 0.7 3.11885 9.80759 1 −0.97077 9.75228 −0.044 −20.7631 7.32746 0.8 3.73162 11.067 1 −1.57943 9.22323 −0.044 −20.8068 7.25835 0.8 4.27927 12.2734 1 −2.23639 8.69929 −0.044 −20.8578 7.151 0.8 4.77221 13.4149 1 −2.94251 8.19135 −0.044 −20.8881 6.97008 0.8 5.21595 14.483 1 −3.69702 7.71032 −0.044 −20.8378 6.71951 0.8 5.61466 15.471 1 −4.49688 7.26596 −0.044 −20.7298 6.40369 0.8 5.97233 16.3737 1 −5.33738 6.86729 −0.044 −20.57 6.01883 0.8 6.29148 17.1876 1 −6.21217 6.52212 −0.044 −20.345 5.569 0.8 6.57329 17.9107 1 −7.11263 6.23401 −0.044 −20.0535 5.05455 0.8 6.81964 18.5421 1 −8.0294 6.00386 −0.044 −19.6934 4.47694 0.8 7.03139 19.0829 1 −8.95316 5.83095 −0.044 −19.256 3.84355 0.8 7.2099 19.535 1 −9.87491 5.71344 −0.044 −18.7305 3.16566 0.8 7.35344 19.9034 1 −10.7862 5.64945 −0.044 −18.1082 2.45662 0.8 7.47192 20.1899 1 −11.679 5.63717 −0.044 −17.3816 1.73224 0.8 7.54429 20.4099 1 −12.5456 5.67441 −0.044 −16.544 1.01208 0.8 7.52968 20.5709 1 −13.3788 5.759 −0.044 −15.5898 0.32008 0.8 7.47137 20.6545 1 −14.1708 5.89184 −0.044 −14.5164 −0.31516 0.8 7.40732 20.6996 1 −14.9155 6.06591 −0.044 −13.3245 −0.85836 0.8 7.34915 20.7206 1 −15.6076 6.27383 −0.044 −12.0214 −1.26753 0.8 7.26879 20.726 1 −16.2421 6.51084 −0.044 −10.6253 −1.49655 0.8 7.15036 20.6784 1 −16.8209 6.75719 −0.044 −9.16904 −1.50273 0.8 7.03045 20.5404 1 −17.3459 7.00006 −0.044 −7.69844 −1.26348 0.8 6.90877 20.328 1 −17.8182 7.23136 −0.044 −6.26349 −0.77592 0.8 6.75615 20.0557 1 −18.2405 7.44205 −0.044 −4.90221 −0.07136 0.8 6.56722 19.7216 1 −18.6176 7.62076 −0.044 −3.63654 0.80879 0.8 6.33405 19.3267 1 −18.9524 7.76007 −0.044 −2.4782 1.8266 0.8 6.05074 18.8726 1 −19.2446 7.8585 −0.044 −1.4269 2.94345 0.8 5.72262 18.3551 1 −19.4932 7.91754 −0.044 −0.47432 4.12436 0.8 5.35258 17.7724 1 −19.6977 7.92373 −0.044 0.38602 5.34375 0.8 4.933 17.1306 1 −19.8481 7.87971 −0.044 1.16182 6.57987 0.8 4.4585 16.4358 1 −19.9405 7.81547 −0.044 1.86275 7.81331 0.8 3.92531 15.6944 1 −19.9887 7.76082 −0.044 2.49857 9.0274 0.8 3.33076 14.9131 1 −20.0156 7.71856 −0.044 3.07588 10.2092 0.8 2.67285 14.0996 1 −19.9917 7.59504 0 3.60043 11.3478 0.8 1.9491 13.2634 1 −20.0234 7.5416 0 4.07885 12.4329 0.8 1.15723 12.4153 1 −20.0556 7.45716 0 4.51482 13.4568 0.8 0.29642 11.5662 1 −20.0735 7.31889 0 4.9114 14.4131 0.8 −0.63966 10.7355 1 −20.0463 7.12654 0 5.27125 15.2963 0.8 −1.66353 9.95485 1 −19.9577 6.88879 0 5.59615 16.1024 0.8 −2.7779 9.25377 1 −19.8105 6.60835 0 5.88717 16.8287 0.8 −3.98336 8.67201 1 −19.6093 6.28329 0 6.14503 17.4736 0.8 −5.2718 8.25858 1 −19.3498 5.9163 0 6.37034 18.0369 0.8 −6.61165 8.02345 1 −19.0293 5.51019 0 6.56382 18.5194 0.8 −7.9693 7.94297 1 −18.6489 5.06562 0 6.7269 18.9228 0.8 −9.32024 8.00207 1 −18.2066 4.58672 0 6.85735 19.2517 0.8 −10.6458 8.17657 1 −17.6978 4.08141 0 6.96676 19.5067 0.8 −11.9341 8.43725 1 −17.1184 3.55935 0 7.0225 19.7063 0.8 −13.1794 8.75319 1 −16.4648 3.03224 0 6.99468 19.8483 0.8 −14.3772 9.10417 1 −15.7336 2.51459 0 6.93824 19.9201 0.8 −15.5233 9.47607 1 −14.9224 2.02401 0 6.88045 19.9598 0.8 −16.6155 9.85339 1 −14.031 1.5806 0 6.82828 19.9799 0.8 −17.6536 10.2183 1 −13.0623 1.20713 0 6.75597 19.9886 0.8 −18.6372 10.5557 1 −12.0237 0.92813 0 6.64499 19.9569 0.8 −19.5756 10.8187 1 −10.9284 0.76864 0 6.5251 19.843 0.8 −20.4681 10.9691 1 −9.79599 0.75085 0 6.41234 19.6525 0.8 −21.3001 10.9895 1 −8.65239 0.88927 0 6.27148 19.4078 0.8 −22.05 10.8883 1 −7.52597 1.1869 0 6.09756 19.1074 0.8 −22.6995 10.6902 1 −6.44314 1.63476 0 5.88807 18.7495 0.8 −23.2417 10.4322 1 −5.42358 2.21285 0 5.64191 18.3327 0.8 −23.6796 10.1486 1 −4.47696 2.89338 0 5.35885 17.8563 0.8 −24.0214 9.8657 1 −3.60441 3.64746 0 5.03875 17.3203 0.8 −24.2771 9.60159 1 −2.80412 4.45135 0 4.68064 16.7265 0.8 −24.4593 9.37021 1 −2.07222 5.28493 0 4.28332 16.0776 0.8 −24.5831 9.18175 1 −1.40001 6.12811 0 3.8457 15.3772 0.8 −24.6627 9.04088 1 −0.78122 6.96613 0 3.36664 14.6296 0.8 −24.71 8.94728 1 −0.21205 7.78806 0 2.8444 13.8406 0.8 −24.7404 8.88186 1 0.31296 8.58323 0 2.27714 13.0169 0.8 −25.2575 8.97437 1.024 0.79819 9.3429 0 1.66234 12.1665 0.8 −25.2954 8.89018 1.024 1.24521 10.061 0 0.99642 11.2992 0.8 −25.344 8.7651 1.024 1.65607 10.7321 0 0.27677 10.4255 0.8 −25.4029 8.56654 1.024 2.03208 11.3519 0 −0.49926 9.55747 0.8 −25.4513 8.28207 1.024 2.37369 11.9173 0 −1.33591 8.71031 0.8 −25.4557 7.90524 1.024 2.68109 12.4264 0 −2.23695 7.90195 0.8 −25.3824 7.44054 1.024 2.95437 12.8782 0 −3.20197 7.14945 0.8 −25.21 6.8995 1.024 3.19363 13.2724 0 −4.22771 6.47022 0.8 −24.9354 6.29094 1.024 3.39922 13.6098 0 −5.30822 5.88257 0.8 −24.5544 5.62356 1.024 3.57148 13.8921 0 −6.43261 5.40165 0.8 −24.0623 4.90727 1.024 3.71399 14.1202 0 −7.58533 5.03661 0.8 −23.4574 4.15108 1.024 3.81962 14.3028 0 −8.74847 4.79129 0.8 −22.7324 3.37083 1.024 3.85666 14.4559 0 −9.90342 4.66458 0.8 −21.8765 2.59021 1.024 3.83096 14.5628 0 −11.0321 4.64997 0.8 −20.883 1.83616 1.024 3.79094 14.6195 0 −12.1184 4.7357 0.8 −19.7508 1.13696 1.024 3.75092 14.6547 0 −13.1494 4.90646 0.8 −18.4847 0.52054 1.024 3.71325 14.6776 0 −14.116 5.14314 0.8 −17.096 0.01199 1.024 3.6595 14.6976 0 −15.013 5.42532 0.8 −15.6025 −0.37175 1.024 3.56865 14.7018 0 −15.8383 5.73486 0.8 −14.025 −0.6227 1.024 3.44929 14.6497 0 −16.591 6.05645 0.8 −12.3851 −0.74126 1.024 3.32395 14.5284 0 −17.2723 6.37645 0.8 −10.7029 −0.73344 1.024 3.18266 14.3566 0 −17.8843 6.68254 0.8 −8.99961 −0.57097 1.024 3.00693 14.1471 0 −18.431 6.96235 0.8 −7.30116 −0.23917 1.024 2.80084 13.8936 0 −18.9197 7.19912 0.8 −5.64646 0.30068 1.024 2.5589 13.5988 0 −19.3544 7.38254 0.8 −4.09041 1.08141 1.024 2.28073 13.2623 0 −19.7355 7.5083 0.8 −2.66697 2.06763 1.024 1.9658 12.8846 0 −20.0618 7.57194 0.8 −1.40706 3.22821 1.024 1.61407 12.4666 0 −20.3281 7.56975 0.8 −0.29656 4.49536 1.024 1.22433 12.0112 0 −20.5245 7.51492 0.8 0.69106 5.81428 1.024 0.795 11.5223 0 −20.6507 7.44085 0.8 1.57624 7.14919 1.024 0.32491 11.0044 0 −20.7213 7.37753 0.8 2.36693 8.47925 1.024 −0.18757 10.4631 0 −20.7631 7.32746 0.8 3.07249 9.78593 1.024 −0.74499 9.90623 0 −20.8361 7.39167 0.825 3.70137 11.0539 1.024 −1.34882 9.34157 0 −20.8772 7.32066 0.825 4.26225 12.2697 1.024 −2.0005 8.77824 0 −20.93 7.21377 0.825 4.76624 13.4206 1.024 −2.70133 8.22693 0 −20.9673 7.03357 0.825 5.21961 14.4979 1.024 −3.45111 7.6985 0 −20.9166 6.78225 0.825 5.62695 15.4946 1.024 −4.24751 7.20294 0 −20.8062 6.46614 0.825 5.99243 16.4052 1.024 −5.08667 6.74994 0 −20.6458 6.08015 0.825 6.31837 17.2263 1.024 −5.96304 6.34824 0 −20.4186 5.62967 0.825 6.60678 17.9556 1.024 −6.86869 6.00313 0 −20.1234 5.11516 0.825 6.85844 18.5926 1.024 −7.79471 5.71784 0 −19.7589 4.53784 0.825 7.07418 19.1384 1.024 −8.73179 5.49413 0 −19.316 3.90527 0.825 7.25533 19.595 1.024 −9.67051 5.33238 0 −18.7844 3.22875 0.825 7.40146 19.9669 1.024 −10.6016 5.23251 0 −18.1555 2.52164 0.825 7.52187 20.2561 1.024 −11.5162 5.1943 0 −17.4219 1.79969 0.825 7.5964 20.478 1.024 −12.4051 5.21682 0 −16.5772 1.08242 0.825 7.58387 20.6408 1.024 −13.2598 5.29797 0 −15.6162 0.39365 0.825 7.52544 20.7257 1.024 −14.0714 5.43595 0 −14.5362 −0.2381 0.825 7.46085 20.7714 1.024 −14.8328 5.62244 0 −13.3381 −0.77748 0.825 7.4029 20.7925 1.024 −15.5387 5.84733 0 −12.0293 −1.1828 0.825 7.32279 20.7978 1.024 −16.1847 6.10173 0 −10.6282 −1.4091 0.825 7.20459 20.7508 1.024 −16.772 6.36819 0 −9.16741 −1.41412 0.825 7.08427 20.6139 1.024 −17.3022 6.63356 0 −7.691 −1.18158 0.825 6.96353 20.4018 1.024 −17.7769 6.88913 0 −6.24675 −0.70685 0.825 6.81186 20.13 1.024 −18.1987 7.12611 0 −4.8755 −0.01124 0.825 6.62128 19.7981 1.024 −18.5721 7.3349 0 −3.5993 0.86218 0.825 6.38583 19.4062 1.024 −18.902 7.50616 0 −2.43259 1.87776 0.825 6.09961 18.9559 1.024 −19.19 7.63641 0 −1.3744 2.99472 0.825 5.76386 18.4455 1.024 −19.4356 7.72743 0 −0.41614 4.17716 0.825 5.38175 17.8732 1.024 −19.6426 7.76169 0 0.4486 5.39917 0.825 4.9453 17.2456 1.024 −19.8014 7.73791 0 1.22758 6.6387 0.825 4.44966 16.5689 1.024 −19.9038 7.6849 0 1.93106 7.8758 0.825 3.89186 15.8493 1.024 −19.9595 7.63513 0 2.56878 9.09375 0.825 3.27 15.0934 1.024 −19.9917 7.59504 0 3.14735 10.2796 0.825 2.58237 14.3092 1.024 −19.9631 7.34883 0.1 3.67265 11.4221 0.825 1.82868 13.5044 1.024 −20.006 7.29881 0.1 4.15144 12.5111 0.825 1.00579 12.6913 1.024 −20.0518 7.21478 0.1 4.58761 13.5388 0.825 0.11122 11.8834 1.024 −20.0808 7.06993 0.1 4.98426 14.4985 0.825 −0.85399 11.0927 1.024 −20.0535 6.86592 0.1 5.34407 15.3849 0.825 −1.90283 10.3527 1.024 −19.9601 6.61385 0.1 5.66888 16.194 0.825 −3.03057 9.68114 1.024 −19.8118 6.31284 0.1 5.95979 16.923 0.825 −4.23908 9.11527 1.024 −19.6117 5.96067 0.1 6.21754 17.5703 0.825 −5.52202 8.69819 1.024 −19.3565 5.55858 0.1 6.44277 18.1357 0.825 −6.85311 8.43847 1.024 −19.0418 5.10974 0.1 6.63619 18.6199 0.825 −8.20478 8.33146 1.024 −18.6654 4.61715 0.1 6.79919 19.0248 0.825 −9.55272 8.35408 1.024 −18.2239 4.08599 0.1 6.92962 19.355 0.825 −10.8801 8.47582 1.024 −17.7114 3.52515 0.1 7.03906 19.6109 0.825 −12.1758 8.6715 1.024 −17.1217 2.94632 0.1 7.09517 19.8111 0.825 −13.4333 8.915 1.024 −16.4509 2.36199 0.1 7.06745 19.9536 0.825 −14.6474 9.18757 1.024 −15.6948 1.78807 0.1 7.01084 20.0255 0.825 −15.8125 9.48055 1.024 −14.849 1.24629 0.1 6.95284 20.0653 0.825 −16.9246 9.78103 1.024 −13.9125 0.76069 0.1 6.90053 20.0854 0.825 −17.9813 10.0758 1.024 −12.8876 0.36132 0.1 6.82808 20.0939 0.825 −18.9803 10.3524 1.024 −11.783 0.0818 0.1 6.71701 20.0619 0.825 −19.9265 10.5731 1.024 −10.6172 −0.04581 0.1 6.59725 19.9474 0.825 −20.8188 10.7076 1.024 −9.41825 0.00232 0.1 6.48463 19.7564 0.825 −21.6478 10.7441 1.024 −8.22012 0.23496 0.1 6.34384 19.511 0.825 −22.4 10.6877 1.024 −7.05534 0.64372 0.1 6.16988 19.2099 0.825 −23.0634 10.5524 1.024 −5.94924 1.2076 0.1 5.96012 18.8513 0.825 −23.6305 10.3607 1.024 −4.91798 1.8994 0.1 5.71345 18.4339 0.825 −24.099 10.1348 1.024 −3.96679 2.68746 0.1 5.42962 17.9567 0.825 −24.4707 9.895 1.024 −3.09284 3.54141 0.1 5.10862 17.42 0.825 −24.7515 9.65943 1.024 −2.29308 4.43853 0.1 4.7493 16.8256 0.825 −24.9525 9.44547 1.024 −1.56165 5.35852 0.1 4.35036 16.1761 0.825 −25.0885 9.26647 1.024 −0.89066 6.28325 0.1 3.91068 15.4752 0.825 −25.1749 9.13023 1.024 −0.27342 7.19825 0.1 3.42906 14.7274 0.825 −25.2255 9.03874 1.024 0.29474 8.09224 0.1 2.9037 13.9385 0.825 −25.2575 8.97437 1.024 0.8178 8.95574 0.1 2.3327 13.1152 0.825 −25.7687 9.06481 1.048 1.30076 9.77969 0.1 1.71342 12.2657 0.825 −25.8088 8.98056 1.048 1.74572 10.5577 0.1 1.04259 11.3998 0.825 −25.8593 8.85477 1.048 2.15401 11.2846 0.1 0.31716 10.5283 0.825 −25.918 8.6539 1.048 2.52701 11.9559 0.1 −0.46618 9.66408 0.825 −25.9584 8.36517 1.048 2.86575 12.5684 0.1 −1.31129 8.82239 0.825 −25.9395 7.98488 1.048 3.17045 13.12 0.1 −2.22126 8.02086 0.825 −25.8306 7.52219 1.048 3.44113 13.6096 0.1 −3.19562 7.27692 0.825 −25.6268 6.98587 1.048 3.67795 14.0369 0.1 −4.23099 6.60847 0.825 −25.3232 6.38349 1.048 3.88138 14.4028 0.1 −5.32085 6.03367 0.825 −24.918 5.7212 1.048 4.05211 14.7088 0.1 −6.45367 5.56726 0.825 −24.4108 5.00443 1.048 4.19259 14.9567 0.1 −7.61337 5.21759 0.825 −23.7954 4.24378 1.048 4.29864 15.1534 0.1 −8.78169 4.98717 0.825 −23.0621 3.45619 1.048 4.3386 15.3155 0.1 −9.94008 4.87376 0.825 −22.2013 2.66323 1.048 4.31281 15.4291 0.1 −11.0708 4.86997 0.825 −21.2066 1.88956 1.048 4.26951 15.4885 0.1 −12.1585 4.9635 0.825 −20.0743 1.16445 1.048 4.22591 15.5244 0.1 −13.1905 5.13913 0.825 −18.8059 0.52 1.048 4.18496 15.5468 0.1 −14.1584 5.37778 0.825 −17.4106 −0.01455 1.048 4.12685 15.5644 0.1 −15.0572 5.65977 0.825 −15.9055 −0.41715 1.048 4.03066 15.5604 0.1 −15.8848 5.96748 0.825 −14.3123 −0.67454 1.048 3.91014 15.4934 0.1 −16.6406 6.28567 0.825 −12.6546 −0.78347 1.048 3.78666 15.3561 0.1 −17.3257 6.60043 0.825 −10.9553 −0.75238 1.048 3.64577 15.1674 0.1 −17.9426 6.89937 0.825 −9.2363 −0.56872 1.048 3.46882 14.9383 0.1 −18.496 7.16832 0.825 −7.52079 −0.23072 1.048 3.26103 14.6617 0.1 −18.9921 7.39154 0.825 −5.84591 0.30533 1.048 3.01885 14.3388 0.1 −19.4347 7.55711 0.825 −4.26361 1.07362 1.048 2.74066 13.9697 0.1 −19.823 7.66117 0.825 −2.8009 2.03369 1.048 2.42607 13.5548 0.1 −20.154 7.6981 0.825 −1.48378 3.15647 1.048 2.07509 13.0952 0.1 −20.4192 7.66882 0.825 −0.31991 4.39882 1.048 1.6869 12.5932 0.1 −20.6097 7.59516 0.825 0.70753 5.70872 1.048 1.26026 12.0523 0.1 −20.7301 7.51148 0.825 1.61168 7.05091 1.048 0.79407 11.477 0.1 −20.7968 7.44387 0.825 2.40434 8.39843 1.048 0.28673 10.8726 0.1 −20.8361 7.39167 0.825 3.10226 9.72662 1.048 −0.2638 10.2459 0.1 −20.9985 7.51018 0.85 3.72252 11.0151 1.048 −0.8597 9.60484 0.1 −21.0379 7.43773 0.85 4.27734 12.2489 1.048 −1.50242 8.95787 0.1 −21.085 7.32753 0.85 4.77858 13.4152 1.048 −2.19395 8.31527 0.1 −21.1296 7.14799 0.85 5.23243 14.5054 1.048 −2.93517 7.68785 0.1 −21.1131 6.89081 0.85 5.64275 15.5129 1.048 −3.72521 7.08623 0.1 −21.0077 6.57112 0.85 6.0126 16.4328 1.048 −4.56196 6.52133 0.1 −20.8456 6.1835 0.85 6.34379 17.2616 1.048 −5.44161 6.00375 0.1 −20.6137 5.73245 0.85 6.63727 17.9976 1.048 −6.35804 5.54232 0.1 −20.3072 5.22099 0.85 6.89332 18.6405 1.048 −7.30376 5.14493 0.1 −19.9284 4.64866 0.85 7.11319 19.1912 1.048 −8.26999 4.81831 0.1 −19.4702 4.02213 0.85 7.2975 19.6521 1.048 −9.24676 4.56751 0.1 −18.923 3.35239 0.85 7.44674 20.0272 1.048 −10.2233 4.39644 0.1 −18.2789 2.65231 0.85 7.56943 20.3189 1.048 −11.1883 4.3082 0.1 −17.534 1.9344 0.85 7.64685 20.5424 1.048 −12.1297 4.30419 0.1 −16.6828 1.21588 0.85 7.63648 20.7071 1.048 −13.0352 4.38224 0.1 −15.7162 0.52418 0.85 7.57868 20.7937 1.048 −13.8932 4.53543 0.1 −14.631 −0.11146 0.85 7.51367 20.8402 1.048 −14.6946 4.75144 0.1 −13.4281 −0.6569 0.85 7.45567 20.8614 1.048 −15.4334 5.01464 0.1 −12.1144 −1.07055 0.85 7.37546 20.8668 1.048 −16.107 5.30893 0.1 −10.7077 −1.30783 0.85 7.25709 20.8197 1.048 −16.7152 5.61901 0.1 −9.23934 −1.32646 0.85 7.13663 20.6826 1.048 −17.2595 5.93178 0.1 −7.75304 −1.10712 0.85 7.01658 20.4698 1.048 −17.7414 6.23754 0.1 −6.29604 −0.64614 0.85 6.86494 20.1975 1.048 −18.1629 6.52854 0.1 −4.90998 0.0378 0.85 6.67064 19.8672 1.048 −18.529 6.79529 0.1 −3.61297 0.89471 0.85 6.43005 19.4778 1.048 −18.8472 7.02671 0.1 −2.42757 1.9009 0.85 6.14025 19.0289 1.048 −19.1238 7.2151 0.1 −1.35422 3.01445 0.85 5.79512 18.5238 1.048 −19.3597 7.36084 0.1 −0.38418 4.19752 0.85 5.39482 17.9629 1.048 −19.5659 7.44326 0.1 0.48951 5.42275 0.85 4.93576 17.3505 1.048 −19.7355 7.45578 0.1 1.27521 6.66706 0.85 4.40997 16.6955 1.048 −19.8534 7.42391 0.1 1.98387 7.90974 0.85 3.81417 16.0054 1.048 −19.9217 7.38412 0.1 2.62557 9.13368 0.85 3.14692 15.2875 1.048 −19.9631 7.34883 0.1 3.2072 10.3257 0.85 2.41027 14.5472 1.048 −19.9665 7.16215 0.2 3.73473 11.4744 0.85 1.60948 13.7872 1.048 −20.0171 7.11485 0.2 4.21515 12.5695 0.85 0.75104 13.0094 1.048 −20.0724 7.03065 0.2 4.65262 13.6028 0.85 −0.15547 12.2125 1.048 −20.1083 6.87944 0.2 5.05029 14.568 0.85 −1.11235 11.4091 1.048 −20.0813 6.66458 0.2 5.41091 15.4595 0.85 −2.15296 10.6548 1.048 −19.9849 6.3987 0.2 5.73637 16.2732 0.85 −3.27727 9.97412 1.048 −19.8394 6.07702 0.2 6.02784 17.0064 0.85 −4.48398 9.40029 1.048 −19.6382 5.70139 0.2 6.28611 17.6574 0.85 −5.76329 8.96664 1.048 −19.3815 5.27114 0.2 6.5118 18.226 0.85 −7.09037 8.67858 1.048 −19.0696 4.78611 0.2 6.70562 18.713 0.85 −8.43976 8.52869 1.048 −18.6959 4.25154 0.2 6.86895 19.1202 0.85 −9.78923 8.49417 1.048 −18.2525 3.67583 0.2 6.99966 19.4523 0.85 −11.1229 8.54695 1.048 −17.7326 3.06874 0.2 7.10939 19.7096 0.85 −12.4297 8.66483 1.048 −17.1305 2.44169 0.2 7.16626 19.9107 0.85 −13.702 8.82685 1.048 −16.4408 1.80904 0.2 7.13879 20.054 0.85 −14.9333 9.01772 1.048 −15.6579 1.18898 0.2 7.08205 20.1265 0.85 −16.1168 9.23275 1.048 −14.7776 0.60433 0.2 7.02372 20.1664 0.85 −17.2475 9.46119 1.048 −13.7973 0.08421 0.2 6.97112 20.1866 0.85 −18.3198 9.69953 1.048 −12.7188 −0.33533 0.2 6.89827 20.1949 0.85 −19.3312 9.93301 1.048 −11.5529 −0.61382 0.2 6.78683 20.162 0.85 −20.2812 10.1429 1.048 −10.323 −0.71278 0.2 6.66715 20.0462 0.85 −21.1709 10.3006 1.048 −9.06511 −0.60679 0.2 6.55417 19.8541 0.85 −21.9963 10.3949 1.048 −7.82002 −0.29292 0.2 6.4124 19.6077 0.85 −22.7513 10.42 1.048 −6.62265 0.20995 0.2 6.23707 19.3054 0.85 −23.4277 10.3745 1.048 −5.49615 0.87105 0.2 6.02589 18.9452 0.85 −24.0172 10.2658 1.048 −4.45343 1.65817 0.2 5.77854 18.5253 0.85 −24.5135 10.1082 1.048 −3.49635 2.53726 0.2 5.49369 18.0455 0.85 −24.9133 9.91752 1.048 −2.61912 3.47691 0.2 5.1709 17.5063 0.85 −25.2185 9.7137 1.048 −1.81711 4.45442 0.2 4.80896 16.9093 0.85 −25.4385 9.51867 1.048 −1.08436 5.45041 0.2 4.40678 16.2573 0.85 −25.587 9.34954 1.048 −0.4129 6.44737 0.2 3.9633 15.5539 0.85 −25.6806 9.21787 1.048 0.20481 7.43061 0.2 3.47722 14.8037 0.85 −25.7347 9.1283 1.048 0.77263 8.38951 0.2 2.94662 14.0126 0.85 −25.7687 9.06481 1.048 1.29461 9.31451 0.2 2.36941 13.1874 0.85 −26.2809 9.15526 1.071 1.77642 10.1962 0.2 1.74286 12.3368 0.85 −26.323 9.07105 1.071 2.21949 11.0285 0.2 1.06349 11.4705 0.85 −26.3756 8.94472 1.071 2.62564 11.8059 0.2 0.32784 10.6002 0.85 −26.434 8.74175 1.071 2.99644 12.5238 0.2 −0.46836 9.73978 0.85 −26.4667 8.44933 1.071 3.33276 13.1789 0.2 −1.32809 8.9044 0.85 −26.4257 8.06723 1.071 3.63492 13.769 0.2 −2.25348 8.11134 0.85 −26.2831 7.60918 1.071 3.9032 14.2928 0.2 −3.24425 7.379 0.85 −26.0496 7.07929 1.071 4.13795 14.7501 0.2 −4.29661 6.7258 0.85 −25.7184 6.48443 1.071 4.33959 15.1416 0.2 −5.40304 6.16968 0.85 −25.29 5.82825 1.071 4.50908 15.469 0.2 −6.55108 5.72477 0.85 −24.7685 5.11173 1.071 4.64772 15.7349 0.2 −7.72391 5.39856 0.85 −24.1438 4.34695 1.071 4.75428 15.9444 0.2 −8.90288 5.19268 0.85 −23.4035 3.55221 1.071 4.79707 16.1147 0.2 −10.0693 5.10365 0.85 −22.5389 2.74738 1.071 4.77141 16.2346 0.2 −11.2055 5.12261 0.85 −21.5434 1.9558 1.071 4.72514 16.2965 0.2 −12.2968 5.23606 0.85 −20.4118 1.20679 1.071 4.67832 16.3331 0.2 −13.3313 5.4279 0.85 −19.143 0.53431 1.071 4.6344 16.3551 0.2 −14.3013 5.67849 0.85 −17.7445 −0.02989 1.071 4.5724 16.3705 0.2 −15.2025 5.96879 0.85 −16.2318 −0.45939 1.071 4.47174 16.359 0.2 −16.0328 6.28176 0.85 −14.6264 −0.73487 1.071 4.35054 16.2792 0.2 −16.7922 6.60203 0.85 −12.9534 −0.84636 1.071 4.22844 16.128 0.2 −17.4814 6.91704 0.85 −11.2388 −0.79578 1.071 4.08744 15.9242 0.2 −18.1014 7.21747 0.85 −9.50649 −0.58703 1.071 3.9096 15.6768 0.2 −18.6592 7.48418 0.85 −7.77879 −0.22742 1.071 3.7002 15.3791 0.2 −19.1622 7.69854 0.85 −6.09094 0.32162 1.071 3.45653 15.0311 0.2 −19.6143 7.84435 0.85 −4.49019 1.08925 1.071 3.17754 14.6327 0.2 −20.0126 7.91158 0.85 −3.00351 2.04222 1.071 2.86236 14.1845 0.2 −20.3472 7.90058 0.85 −1.65522 3.15282 1.071 2.51071 13.6878 0.2 −20.6058 7.8298 0.85 −0.45777 4.38498 1.071 2.12239 13.1445 0.2 −20.7859 7.73128 0.85 0.6025 5.68844 1.071 1.69653 12.5579 0.2 −20.8984 7.63613 0.85 1.53702 7.02802 1.071 1.23177 11.9324 0.2 −20.9611 7.56412 0.85 2.35943 8.37464 1.071 0.72691 11.273 0.2 −20.9985 7.51018 0.85 3.08732 9.70255 1.071 0.17963 10.5867 0.2 −21.3705 7.72492 0.875 3.73387 10.9929 1.071 −0.41187 9.88071 0.2 −21.4098 7.65141 0.875 4.3086 12.2314 1.071 −1.04923 9.16323 0.2 −21.4558 7.53929 0.875 4.8233 13.4047 1.071 −1.73495 8.44443 0.2 −21.4999 7.35754 0.875 5.28557 14.5033 1.071 −2.47062 7.7351 0.2 −21.5094 7.09714 0.875 5.70008 15.52 1.071 −3.25669 7.04652 0.2 −21.4457 6.76286 0.875 6.07111 16.4493 1.071 −4.09242 6.39054 0.2 −21.2964 6.3651 0.875 6.40177 17.2873 1.071 −4.97544 5.77912 0.2 −21.0728 5.90368 0.875 6.6937 18.0318 1.071 −5.90157 5.22399 0.2 −20.7653 5.38507 0.875 6.94872 18.6821 1.071 −6.8648 4.73662 0.2 −20.3749 4.81142 0.875 7.16749 19.2391 1.071 −7.85709 4.32748 0.2 −19.9006 4.18616 0.875 7.35057 19.7054 1.071 −8.86832 4.00557 0.2 −19.3335 3.52048 0.875 7.49917 20.0848 1.071 −9.8866 3.77835 0.2 −18.6665 2.82759 0.875 7.62088 20.3801 1.071 −10.8985 3.65165 0.2 −17.8947 2.12147 0.875 7.69879 20.6057 1.071 −11.8889 3.62825 0.2 −17.0147 1.41853 0.875 7.6878 20.7719 1.071 −12.8422 3.7055 0.2 −16.0241 0.73835 0.875 7.62986 20.8596 1.071 −13.7439 3.87323 0.2 −14.9218 0.1044 0.875 7.5642 20.9065 1.071 −14.5834 4.11427 0.2 −13.7084 −0.45327 0.875 7.50581 20.9279 1.071 −15.3545 4.40864 0.2 −12.3884 −0.89693 0.875 7.425 20.9327 1.071 −16.055 4.73675 0.2 −10.9734 −1.17691 0.875 7.30637 20.8838 1.071 −16.6851 5.08192 0.2 −9.49014 −1.24245 0.875 7.18542 20.7455 1.071 −17.2455 5.43163 0.2 −7.98157 −1.06443 0.875 7.06299 20.532 1.071 −17.7371 5.77671 0.2 −6.49625 −0.63877 0.875 6.90701 20.2596 1.071 −18.1613 6.1092 0.2 −5.0796 0.02093 0.875 6.70325 19.9319 1.071 −18.524 6.41852 0.2 −3.74697 0.85429 0.875 6.44959 19.5469 1.071 −18.8351 6.69169 0.2 −2.52553 1.84399 0.875 6.14695 19.102 1.071 −19.104 6.91913 0.2 −1.42085 2.95081 0.875 5.78876 18.6008 1.071 −19.3347 7.09782 0.2 −0.42461 4.13414 0.875 5.36775 18.0491 1.071 −19.54 7.20959 0.2 0.4704 5.36455 0.875 4.8797 17.4524 1.071 −19.7153 7.24539 0.2 1.27273 6.6176 0.875 4.31932 16.8188 1.071 −19.8425 7.22696 0.2 1.99478 7.87086 0.875 3.68587 16.1542 1.071 −19.9188 7.19385 0.2 2.64721 9.10646 0.875 2.97984 15.4644 1.071 −19.9665 7.16215 0.2 3.23755 10.3105 0.875 2.20785 14.75 1.071 −20.0069 7.0378 0.3 3.7718 11.4716 0.875 1.37947 14.0084 1.071 −20.0628 6.99175 0.3 4.2575 12.5788 0.875 0.50478 13.2365 1.071 −20.1245 6.90658 0.3 4.69929 13.6239 0.875 −0.40902 12.435 1.071 −20.1654 6.74946 0.3 5.10054 14.6 0.875 −1.36917 11.6217 1.071 −20.1382 6.5249 0.3 5.46417 15.5018 0.875 −2.41491 10.8589 1.071 −20.0381 6.24692 0.3 5.7922 16.3249 0.875 −3.54239 10.1656 1.071 −19.8916 5.90848 0.3 6.08595 17.0666 0.875 −4.75062 9.57312 1.071 −19.6891 5.51201 0.3 6.34627 17.7252 0.875 −6.03003 9.1108 1.071 −19.4313 5.0565 0.3 6.57372 18.3004 0.875 −7.35722 8.78076 1.071 −19.1185 4.54162 0.3 6.76908 18.793 0.875 −8.70886 8.57428 1.071 −18.7429 3.97318 0.3 6.93371 19.2049 0.875 −10.0644 8.47041 1.071 −18.2942 3.36087 0.3 7.06551 19.5408 0.875 −11.4083 8.44512 1.071 −17.7643 2.71554 0.3 7.17611 19.8012 0.875 −12.7293 8.4806 1.071 −17.1471 2.04941 0.3 7.23464 20.0042 0.875 −14.0181 8.56476 1.071 −16.4363 1.37799 0.3 7.20807 20.1493 0.875 −15.2666 8.69076 1.071 −15.626 0.72092 0.3 7.15115 20.2229 0.875 −16.4669 8.85446 1.071 −14.7112 0.10296 0.3 7.09221 20.2634 0.875 −17.6126 9.04709 1.071 −13.6887 −0.44347 0.3 7.03892 20.2837 0.875 −18.6978 9.26157 1.071 −12.5604 −0.8776 0.3 6.96511 20.2916 0.875 −19.7185 9.48766 1.071 −11.3388 −1.1529 0.3 6.85268 20.257 0.875 −20.674 9.70428 1.071 −10.052 −1.22619 0.3 6.733 20.1383 0.875 −21.5627 9.90008 1.071 −8.74226 −1.07187 0.3 6.6186 19.9438 0.875 −22.3842 10.0586 1.071 −7.45583 −0.69186 0.3 6.4741 19.6948 0.875 −23.1374 10.1652 1.071 −6.22902 −0.11262 0.3 6.29535 19.3894 0.875 −23.8189 10.2065 1.071 −5.08286 0.62779 0.3 6.08099 19.025 0.875 −24.4219 10.1777 1.071 −4.02739 1.49304 0.3 5.83152 18.5993 0.875 −24.9383 10.0857 1.071 −3.06208 2.44761 0.3 5.54375 18.1132 0.875 −25.3608 9.94282 1.071 −2.179 3.45932 0.3 5.21654 17.5674 0.875 −25.6876 9.77018 1.071 −1.37261 4.5055 0.3 4.8489 16.9637 0.875 −25.9253 9.59368 1.071 −0.63672 5.56711 0.3 4.44004 16.3046 0.875 −26.0861 9.43393 1.071 0.03683 6.62686 0.3 3.98881 15.5938 0.875 −26.187 9.30629 1.071 0.65562 7.6702 0.3 3.49367 14.8361 0.875 −26.2449 9.21821 1.071 1.22383 8.6863 0.3 2.95249 14.0377 0.875 −26.2809 9.15526 1.071 1.7455 9.66557 0.3 2.36293 13.2059 0.875 −26.7931 9.24571 1.095 2.2264 10.5986 0.3 1.7218 12.3496 0.875 −26.8373 9.16149 1.095 2.668 11.4791 0.3 1.02535 11.4793 0.875 −26.8919 9.03451 1.095 3.07209 12.3014 0.3 0.26978 10.6073 0.875 −26.9501 8.82929 1.095 3.44059 13.0608 0.3 −0.5495 9.74849 0.875 −26.9754 8.53315 1.095 3.7747 13.7537 0.3 −1.43504 8.91844 0.875 −26.9132 8.14997 1.095 4.0748 14.3779 0.3 −2.38901 8.13575 0.875 −26.7384 7.69803 1.095 4.34105 14.932 0.3 −3.41049 7.4197 0.875 −26.476 7.17524 1.095 4.57383 15.4159 0.3 −4.49477 6.78958 0.875 −26.1178 6.58824 1.095 4.77369 15.8303 0.3 −5.63294 6.26364 0.875 −25.6659 5.93831 1.095 4.94194 16.1767 0.3 −6.81082 5.85539 0.875 −25.1291 5.22191 1.095 5.07877 16.4585 0.3 −8.01022 5.57134 0.875 −24.4946 4.45232 1.095 5.18582 16.6795 0.3 −9.2114 5.41151 0.875 −23.7464 3.64986 1.095 5.23125 16.8573 0.3 −10.3951 5.37006 0.875 −22.877 2.83264 1.095 5.20574 16.9828 0.3 −11.5439 5.43431 0.875 −21.8797 2.0228 1.095 5.15688 17.0471 0.3 −12.6435 5.59229 0.875 −20.7478 1.24966 1.095 5.10721 17.0843 0.3 −13.6812 5.8332 0.875 −19.4778 0.549 1.095 5.06074 17.1059 0.3 −14.6513 6.12979 0.875 −18.075 −0.0449 1.095 4.99544 17.1194 0.3 −15.5504 6.4622 0.875 −16.5537 −0.50158 1.095 4.89127 17.1014 0.3 −16.3779 6.81217 0.875 −14.935 −0.79668 1.095 4.76967 17.0112 0.3 −17.134 7.16507 0.875 −13.2456 −0.91547 1.095 4.64869 16.8485 0.3 −17.824 7.50058 0.875 −11.5139 −0.85358 1.095 4.5074 16.6319 0.3 −18.4517 7.80489 0.875 −9.76762 −0.61547 1.095 4.3293 16.3686 0.3 −19.0268 8.05229 0.875 −8.03069 −0.21466 1.095 4.11903 16.0523 0.3 −19.5526 8.22542 0.875 −6.33563 0.36935 1.095 3.87425 15.6828 0.3 −20.0267 8.30651 0.875 −4.72369 1.15509 1.095 3.59418 15.2595 0.3 −20.4355 8.29435 0.875 −3.22414 2.12109 1.095 3.27814 14.7832 0.3 −20.7641 8.21141 0.875 −1.85778 3.23751 1.095 2.92579 14.2549 0.3 −21.0077 8.09151 0.875 −0.63462 4.46876 1.095 2.53691 13.6767 0.3 −21.1733 7.96592 0.875 0.45202 5.77252 1.095 2.11079 13.0518 0.3 −21.2764 7.85809 0.875 1.41156 7.11467 1.095 1.64636 12.3843 0.3 −21.3347 7.78098 0.875 2.25688 8.46588 1.095 1.14234 11.6796 0.3 −21.3705 7.72492 0.875 3.00513 9.80001 1.095 0.59666 10.9439 0.3 −21.9819 8.01247 0.9 3.66991 11.0975 1.095 0.00768 10.1845 0.3 −22.0203 7.93677 0.9 4.26056 12.3438 1.095 −0.62687 9.40992 0.3 −22.0684 7.8232 0.9 4.78909 13.5252 1.095 −1.3095 8.62989 0.3 −22.1233 7.64088 0.9 5.26358 14.6316 1.095 −2.04237 7.85536 0.3 −22.159 7.37802 0.9 5.68879 15.656 1.095 −2.82692 7.09812 0.3 −22.1366 7.03229 0.9 6.06923 16.5924 1.095 −3.66363 6.37093 0.3 −22.0276 6.61376 0.9 6.40829 17.4368 1.095 −4.55138 5.68699 0.3 −21.8249 6.1327 0.9 6.70757 18.1871 1.095 −5.48743 5.06003 0.3 −21.5224 5.59861 0.9 6.96925 18.8423 1.095 −6.46715 4.50425 0.3 −21.1208 5.01741 0.9 7.194 19.4035 1.095 −7.4831 4.033 0.3 −20.6223 4.39308 0.9 7.38196 19.8733 1.095 −8.52497 3.65803 0.3 −20.0254 3.7326 0.9 7.53492 20.2554 1.095 −9.57988 3.38927 0.3 −19.3267 3.04659 0.9 7.66005 20.5528 1.095 −10.6326 3.2344 0.3 −18.5239 2.34691 0.9 7.73984 20.7803 1.095 −11.6656 3.19697 0.3 −17.6142 1.64888 0.9 7.72505 20.9479 1.095 −12.6606 3.27359 0.3 −16.594 0.97376 0.9 7.6661 21.0362 1.095 −13.6009 3.45161 0.3 −15.463 0.3439 0.9 7.60079 21.085 1.095 −14.4748 3.71014 0.3 −14.2247 −0.21724 0.9 7.54258 21.1091 1.095 −15.276 4.02589 0.3 −12.8847 −0.68017 0.9 7.4611 21.1187 1.095 −16.0026 4.37727 0.3 −11.4528 −1.00581 0.9 7.33857 21.0753 1.095 −16.655 4.74647 0.3 −9.94761 −1.14381 0.9 7.21307 20.9376 1.095 −17.2337 5.121 0.3 −8.40425 −1.04593 0.9 7.08462 20.7239 1.095 −17.7386 5.49209 0.3 −6.87198 −0.69026 0.9 6.92004 20.4516 1.095 −18.1713 5.85147 0.3 −5.40159 −0.08277 0.9 6.70378 20.1258 1.095 −18.5379 6.18743 0.3 −4.01909 0.72287 0.9 6.43548 19.7433 1.095 −18.8508 6.48544 0.3 −2.74492 1.69136 0.9 6.11784 19.3001 1.095 −19.1202 6.73532 0.3 −1.5916 2.78876 0.9 5.74359 18.8004 1.095 −19.3516 6.93323 0.3 −0.55336 3.97283 0.9 5.30198 18.253 1.095 −19.5593 7.06091 0.3 0.37752 5.21087 0.9 4.78994 17.6631 1.095 −19.7399 7.10854 0.3 1.20886 6.47713 0.9 4.20336 17.038 1.095 −19.8734 7.09706 0.3 1.95426 7.74702 0.9 3.54443 16.3811 1.095 −19.9551 7.06757 0.3 2.62567 9.0011 0.9 2.81585 15.6958 1.095 −20.0069 7.0378 0.3 3.23181 10.2244 0.9 2.02648 14.9795 1.095 −20.0839 6.97357 0.4 3.77868 11.405 0.9 1.18628 14.2287 1.095 −20.1426 6.92669 0.4 4.27451 12.5316 0.9 0.30336 13.4426 1.095 −20.2076 6.83908 0.4 4.72467 13.5954 0.9 −0.61734 12.6242 1.095 −20.2506 6.67621 0.4 5.13292 14.5893 0.9 −1.58599 11.7949 1.095 −20.222 6.44327 0.4 5.50246 15.5076 0.9 −2.63939 11.0133 1.095 −20.1189 6.15464 0.4 5.83555 16.3459 0.9 −3.77293 10.2961 1.095 −19.9698 5.80229 0.4 6.1337 17.1013 0.9 −4.986 9.67308 1.095 −19.7653 5.38819 0.4 6.39796 17.7721 0.9 −6.26894 9.16848 1.095 −19.5051 4.91158 0.4 6.62879 18.3579 0.9 −7.60012 8.78272 1.095 −19.1887 4.3726 0.4 6.82704 18.8597 0.9 −8.95851 8.5093 1.095 −18.8074 3.77745 0.4 6.99405 19.2793 0.9 −10.3251 8.33495 1.095 −18.3499 3.13637 0.4 7.12794 19.6214 0.9 −11.6842 8.24234 1.095 −17.8073 2.46109 0.4 7.24 19.8867 0.9 −13.0231 8.21867 1.095 −17.1726 1.76489 0.4 7.30121 20.0929 0.9 −14.3316 8.25284 1.095 −16.4391 1.06422 0.4 7.27646 20.241 0.9 −15.6005 8.33605 1.095 −15.6006 0.37987 0.4 7.21923 20.3165 0.9 −16.8215 8.46375 1.095 −14.6518 −0.26158 0.4 7.15929 20.3578 0.9 −17.9872 8.62888 1.095 −13.5894 −0.82539 0.4 7.10493 20.3784 0.9 −19.0911 8.82387 1.095 −12.4157 −1.26737 0.4 7.02961 20.3858 0.9 −20.1274 9.0438 1.095 −11.1447 −1.53668 0.4 6.91564 20.3485 0.9 −21.0922 9.27843 1.095 −9.80847 −1.58712 0.4 6.79589 20.2252 0.9 −21.9823 9.51983 1.095 −8.45414 −1.39335 0.4 6.67916 20.027 0.9 −22.7999 9.74429 1.095 −7.13135 −0.96114 0.4 6.53099 19.7737 0.9 −23.5474 9.93283 1.095 −5.87709 −0.32251 0.4 6.34792 19.4629 0.9 −24.2282 10.0562 1.095 −4.7108 0.47977 0.4 6.12904 19.0916 0.9 −24.8384 10.101 1.095 −3.64052 1.40675 0.4 5.8749 18.6575 0.9 −25.3689 10.0698 1.095 −2.66427 2.42191 0.4 5.58128 18.1621 0.9 −25.8103 9.97188 1.095 −1.77271 3.49247 0.4 5.24677 17.6062 0.9 −26.1565 9.82905 1.095 −0.9598 4.59565 0.4 4.87059 16.9916 0.9 −26.4113 9.67058 1.095 −0.2191 5.71244 0.4 4.45175 16.3209 0.9 −26.5845 9.51969 1.095 0.45775 6.82549 0.4 3.98884 15.5981 0.9 −26.693 9.39553 1.095 1.07851 7.9202 0.4 3.47999 14.8284 0.9 −26.7549 9.30848 1.095 1.64763 8.98547 0.4 2.92284 14.0182 0.9 −26.7931 9.24571 1.095 2.16934 10.0116 0.4 2.31468 13.1753 0.9 −27.2888 9.33333 1.118 2.64946 10.989 0.4 1.65184 12.3093 0.9 −27.335 9.2489 1.118 3.08966 11.9112 0.4 0.9301 11.4317 0.9 −27.3917 9.12094 1.118 3.49195 12.7724 0.4 0.1452 10.5556 0.9 −27.4499 8.91292 1.118 3.85842 13.5678 0.4 −0.70717 9.69669 0.9 −27.4678 8.61254 1.118 4.1904 14.2935 0.4 −1.63006 8.87249 0.9 −27.3855 8.22819 1.118 4.48841 14.9472 0.4 −2.62575 8.10365 0.9 −27.1804 7.78248 1.118 4.75268 15.5277 0.4 −3.69208 7.41067 0.9 −26.89 7.26633 1.118 4.98365 16.0347 0.4 −4.82311 6.81461 0.9 −26.5048 6.68635 1.118 5.18192 16.4689 0.4 −6.00763 6.33428 0.9 −26.0289 6.04147 1.118 5.34907 16.8317 0.4 −7.22908 5.98325 0.9 −25.475 5.32408 1.118 5.48432 17.1272 0.4 −8.46795 5.77317 0.9 −24.8287 4.54806 1.118 5.59173 17.3583 0.4 −9.70129 5.70276 0.9 −24.0702 3.73656 1.118 5.63929 17.5425 0.4 −10.9075 5.75658 0.9 −23.1929 2.90593 1.118 5.6143 17.673 0.4 −12.0699 5.91425 0.9 −22.1902 2.07741 1.118 5.56299 17.7393 0.4 −13.1762 6.15654 0.9 −21.054 1.28047 1.118 5.51076 17.7769 0.4 −14.2179 6.46356 0.9 −19.7783 0.55286 1.118 5.4622 17.7981 0.4 −15.1912 6.81304 0.9 −18.3668 −0.06867 1.118 5.39426 17.8097 0.4 −16.0927 7.19028 0.9 −16.8322 −0.5497 1.118 5.28757 17.7861 0.4 −16.9214 7.58043 0.9 −15.1957 −0.86105 1.118 5.166 17.6875 0.4 −17.6853 7.95467 0.9 −13.4853 −0.98315 1.118 5.0457 17.5158 0.4 −18.3895 8.2951 0.9 −11.7326 −0.90726 1.118 4.90472 17.2887 0.4 −19.0444 8.57233 0.9 −9.96869 −0.63706 1.118 4.72656 17.0126 0.4 −19.6542 8.76068 0.9 −8.22173 −0.18372 1.118 4.51583 16.6813 0.4 −20.2125 8.84289 0.9 −6.5237 0.4579 1.118 4.27037 16.2943 0.4 −20.7025 8.82395 0.9 −4.9086 1.28731 1.118 3.98958 15.8511 0.4 −21.1078 8.72584 0.9 −3.40385 2.28602 1.118 3.67291 15.3521 0.4 −21.4209 8.57975 0.9 −2.02869 3.42639 1.118 3.31989 14.7987 0.4 −21.6469 8.42002 0.9 −0.79006 4.6728 1.118 2.93012 14.1929 0.4 −21.7987 8.27221 0.9 0.31426 5.98938 1.118 2.50313 13.5378 0.4 −21.8936 8.15335 0.9 1.29141 7.34421 1.118 2.03822 12.8375 0.4 −21.948 8.07118 0.9 2.15403 8.70804 1.118 1.53386 12.0972 0.4 −21.9819 8.01247 0.9 2.91856 10.0549 1.118 0.98818 11.3234 0.4 −22.7983 8.34358 0.925 3.59816 11.3652 1.118 0.39938 10.5232 0.4 −22.8341 8.26425 0.925 4.20221 12.6242 1.118 −0.23486 9.70506 0.4 −22.8804 8.14663 0.925 4.74276 13.8178 1.118 −0.91728 8.87887 0.4 −22.9392 7.96051 0.925 5.228 14.936 1.118 −1.65044 8.0557 0.4 −22.9949 7.69436 0.925 5.66276 15.9714 1.118 −2.43652 7.24779 0.4 −23.0215 7.34022 0.925 6.05163 16.918 1.118 −3.277 6.46873 0.4 −22.9804 6.8988 0.925 6.39814 17.7716 1.118 −4.17164 5.73265 0.4 −22.8321 6.38464 0.925 6.70398 18.5302 1.118 −5.11867 5.05467 0.4 −22.574 5.81087 0.925 6.97145 19.1925 1.118 −6.11438 4.45093 0.4 −22.2011 5.19009 0.925 7.20113 19.7599 1.118 −7.15171 3.93677 0.4 −21.7084 4.53593 0.925 7.39321 20.2348 1.118 −8.22002 3.52555 0.4 −21.0981 3.85748 0.925 7.54956 20.6211 1.118 −9.30552 3.22854 0.4 −20.3642 3.17272 0.925 7.67755 20.9216 1.118 −10.3916 3.05425 0.4 −19.5045 2.50012 0.925 7.75796 21.1521 1.118 −11.4592 3.00632 0.4 −18.5322 1.83971 0.925 7.73898 21.3214 1.118 −12.4882 3.08051 0.4 −17.4577 1.19315 0.925 7.67906 21.4106 1.118 −13.4606 3.26254 0.4 −16.2814 0.5789 0.925 7.61379 21.4611 1.118 −14.3642 3.52934 0.4 −15.0034 0.02323 0.925 7.55526 21.4876 1.118 −15.1925 3.85557 0.4 −13.6287 −0.44784 0.925 7.47266 21.5004 1.118 −15.9439 4.21833 0.4 −12.1656 −0.80145 0.925 7.34634 21.4605 1.118 −16.6187 4.59942 0.4 −10.6285 −0.99649 0.925 7.21646 21.3221 1.118 −17.2173 4.98611 0.4 −9.04334 −0.99188 0.925 7.08363 21.1055 1.118 −17.7396 5.36932 0.4 −7.44887 −0.75197 0.925 6.91338 20.8296 1.118 −18.1871 5.74051 0.4 −5.89774 −0.24845 0.925 6.6893 20.5001 1.118 −18.5662 6.08784 0.4 −4.4379 0.49932 0.925 6.4119 20.1131 1.118 −18.8891 6.39637 0.4 −3.09415 1.44047 0.925 6.0839 19.6646 1.118 −19.1674 6.65504 0.4 −1.87676 2.52721 0.925 5.69728 19.1594 1.118 −19.4061 6.8602 0.4 −0.78086 3.71244 0.925 5.24143 18.6064 1.118 −19.6204 6.99291 0.4 0.20109 4.96016 0.925 4.71464 18.0096 1.118 −19.8068 7.04313 0.4 1.07581 6.24305 0.925 4.11516 17.3743 1.118 −19.945 7.03271 0.4 1.85597 7.53518 0.925 3.44551 16.703 1.118 −20.0299 7.00347 0.4 2.55546 8.81459 0.925 2.7095 15.9978 1.118 −20.0839 6.97357 0.4 3.18502 10.0644 0.925 1.91573 15.2564 1.118 −20.1975 6.97078 0.5 3.75111 11.272 0.925 1.07244 14.4772 1.118 −20.2566 6.92089 0.5 4.26241 12.4255 0.925 0.18556 13.6618 1.118 −20.3214 6.82897 0.5 4.72554 13.5152 0.925 −0.74205 12.8161 1.118 −20.3627 6.66034 0.5 5.14475 14.5337 0.925 −1.72136 11.9621 1.118 −20.3318 6.42046 0.5 5.52356 15.475 0.925 −2.78327 11.1502 1.118 −20.2265 6.12265 0.5 5.86459 16.3345 0.925 −3.92542 10.3993 1.118 −20.0748 5.75867 0.5 6.16956 17.1091 0.925 −5.14772 9.73813 1.118 −19.8669 5.33051 0.5 6.43983 17.797 0.925 −6.43999 9.18712 1.118 −19.602 4.83764 0.5 6.67587 18.3977 0.925 −7.7825 8.74857 1.118 −19.2789 4.2804 0.5 6.87855 18.9123 0.925 −9.15526 8.41798 1.118 −18.8886 3.66537 0.5 7.04924 19.3426 0.925 −10.5396 8.18417 1.118 −18.419 3.00334 0.5 7.1863 19.6933 0.925 −11.9194 8.03331 1.118 −17.8607 2.30675 0.5 7.30051 19.9655 0.925 −13.2819 7.95482 1.118 −17.2061 1.58967 0.5 7.36544 20.1763 0.925 −14.6156 7.94111 1.118 −16.4483 0.86948 0.5 7.34368 20.3287 0.925 −15.9108 7.98363 1.118 −15.5811 0.16806 0.5 7.28601 20.4068 0.925 −17.1582 8.07805 1.118 −14.5992 −0.48686 0.5 7.22469 20.4493 0.925 −18.3496 8.21857 1.118 −13.4996 −1.05899 0.5 7.16862 20.4702 0.925 −19.4778 8.39803 1.118 −12.2854 −1.50215 0.5 7.09096 20.4768 0.925 −20.5347 8.6182 1.118 −10.9723 −1.76328 0.5 6.97463 20.4353 0.925 −21.513 8.87652 1.118 −9.59455 −1.79465 0.5 6.85479 20.3051 0.925 −22.4055 9.17077 1.118 −8.20239 −1.5714 0.5 6.7346 20.1009 0.925 −23.2162 9.46961 1.118 −6.84731 −1.10176 0.5 6.58168 19.8403 0.925 −23.9564 9.73267 1.118 −5.56655 −0.42088 0.5 6.39301 19.5202 0.925 −24.6334 9.92963 1.118 −4.37877 0.42618 0.5 6.16752 19.1379 0.925 −25.2472 10.039 1.118 −3.29118 1.399 0.5 5.90515 18.6912 0.925 −25.7883 10.0613 1.118 −2.30105 2.46032 0.5 5.6016 18.1816 0.925 −26.2453 10.0034 1.118 −1.39839 3.57685 0.5 5.25556 17.6101 0.925 −26.6093 9.88839 1.118 −0.57688 4.72557 0.5 4.86617 16.9783 0.925 −26.8801 9.74668 1.118 0.17014 5.88715 0.5 4.43188 16.2894 0.925 −27.0657 9.60398 1.118 0.85135 7.044 0.5 3.95094 15.5477 0.925 −27.182 9.48274 1.118 1.47473 8.1813 0.5 3.42101 14.7589 0.925 −27.2482 9.39627 1.118 2.04525 9.28753 0.5 2.83939 13.93 0.925 −27.2888 9.33333 1.118 2.56723 10.3528 0.5 2.20286 13.0693 0.925 −27.7854 9.42095 1.141 3.04668 11.3675 0.5 1.50701 12.1877 0.925 −27.8339 9.33616 1.141 3.48554 12.3248 0.5 0.74702 11.2978 0.925 −27.8927 9.20697 1.141 3.88613 13.2188 0.5 −0.08173 10.4142 0.925 −27.9508 8.99572 1.141 4.2507 14.0444 0.5 −0.98364 9.5542 0.925 −27.9611 8.69066 1.141 4.58065 14.7978 0.5 −1.9631 8.73897 0.925 −27.859 8.30525 1.141 4.87662 15.4765 0.5 −3.02287 7.99373 0.925 −27.625 7.86604 1.141 5.13901 16.0791 0.5 −4.16102 7.34565 0.925 −27.3069 7.35646 1.141 5.36828 16.6055 0.5 −5.36887 6.82146 0.925 −26.894 6.7835 1.141 5.56511 17.0563 0.5 −6.62939 6.44191 0.925 −26.3935 6.14289 1.141 5.73118 17.433 0.5 −7.91831 6.21428 0.925 −25.8204 5.42397 1.141 5.86486 17.7401 0.5 −9.20986 6.13304 0.925 −25.161 4.64009 1.141 5.97261 17.9796 0.5 −10.4812 6.18271 0.925 −24.39 3.81837 1.141 6.02222 18.1693 0.5 −11.7131 6.35194 0.925 −23.5027 2.97316 1.141 5.99723 18.3039 0.5 −12.891 6.62038 0.925 −22.4921 2.12499 1.141 5.94429 18.3722 0.5 −14.0057 6.96359 0.925 −21.3488 1.30369 1.141 5.8901 18.4105 0.5 −15.0464 7.37332 0.925 −20.0644 0.54909 1.141 5.83999 18.4313 0.5 −16.0118 7.82317 0.925 −18.6407 −0.09944 1.141 5.77013 18.4416 0.5 −16.9048 8.28735 0.925 −17.0892 −0.60346 1.141 5.66159 18.4142 0.5 −17.7407 8.72458 0.925 −15.4311 −0.92885 1.141 5.54028 18.3093 0.5 −18.5227 9.11961 0.925 −13.6961 −1.05122 1.141 5.42152 18.1304 0.5 −19.2613 9.44106 0.925 −11.919 −0.95757 1.141 5.2804 17.8957 0.5 −19.9656 9.64202 0.925 −10.1351 −0.65118 1.141 5.10289 17.6096 0.5 −20.6202 9.70208 0.925 −8.3769 −0.14099 1.141 4.89219 17.267 0.5 −21.1968 9.62938 0.925 −6.67605 0.56423 1.141 4.64654 16.8669 0.5 −21.6726 9.46012 0.925 −5.06114 1.44953 1.141 4.36536 16.4088 0.5 −22.0435 9.24365 0.925 −3.55787 2.49649 1.141 4.04815 15.893 0.5 −22.3172 9.01631 0.925 −2.18234 3.67618 1.141 3.69444 15.321 0.5 −22.5092 8.80565 0.925 −0.93888 4.95319 1.141 3.30377 14.6949 0.5 −22.6377 8.62925 0.925 0.17441 6.29438 1.141 2.87563 14.0178 0.5 −22.7194 8.49562 0.925 1.16358 7.67009 1.141 2.40932 13.2938 0.5 −22.7675 8.40625 0.925 2.04047 9.05227 1.141 1.90322 12.5283 0.5 −22.7983 8.34358 0.925 2.8196 10.4164 1.141 1.35608 11.7272 0.5 −23.5064 8.58696 0.95 3.51267 11.7435 1.141 0.76537 10.8983 0.5 −23.5409 8.50508 0.95 4.12924 13.0187 1.141 0.12881 10.0501 0.5 −23.5865 8.38427 0.95 4.68144 14.2277 1.141 −0.55643 9.19233 0.5 −23.6468 8.19433 0.95 5.1772 15.3604 1.141 −1.29323 8.33644 0.5 −23.7108 7.92412 0.95 5.62147 16.4092 1.141 −2.08431 7.4951 0.5 −23.7576 7.56447 0.95 6.01886 17.3682 1.141 −2.93192 6.68267 0.5 −23.7464 7.11187 0.95 6.37289 18.233 1.141 −3.83636 5.91405 0.5 −23.625 6.57906 0.95 6.68534 19.0016 1.141 −4.7963 5.2053 0.5 −23.3908 5.9808 0.95 6.95851 19.6727 1.141 −5.80847 4.57386 0.5 −23.0398 5.32985 0.95 7.19293 20.2476 1.141 −6.86577 4.03623 0.5 −22.5619 4.6435 0.95 7.38901 20.7288 1.141 −7.95692 3.60638 0.5 −21.9589 3.93295 0.95 7.54837 21.1203 1.141 −9.06723 3.29564 0.5 −21.2324 3.20992 0.95 7.67906 21.4248 1.141 −10.1791 3.11214 0.5 −20.3784 2.49339 0.95 7.75942 21.6589 1.141 −11.2726 3.05859 0.5 −19.3957 1.80422 0.95 7.73697 21.8303 1.141 −12.3272 3.12962 0.5 −18.2888 1.16027 0.95 7.67601 21.9207 1.141 −13.3246 3.31013 0.5 −17.0636 0.58104 0.95 7.61034 21.9726 1.141 −14.2523 3.5764 0.5 −15.7301 0.08394 0.95 7.55098 22.0007 1.141 −15.1041 3.90244 0.5 −14.3056 −0.33194 0.95 7.46677 22.0156 1.141 −15.8783 4.26498 0.5 −12.8046 −0.66342 0.95 7.33677 21.9775 1.141 −16.5751 4.64559 0.5 −11.2357 −0.86867 0.95 7.2028 21.837 1.141 −17.195 5.03125 0.5 −9.61716 −0.90034 0.95 7.06658 21.6156 1.141 −17.7383 5.41244 0.5 −7.98054 −0.71911 0.95 6.89248 21.3334 1.141 −18.2066 5.78053 0.5 −6.36918 −0.29826 0.95 6.66368 20.9961 1.141 −18.6063 6.12364 0.5 −4.83205 0.36721 0.95 6.38086 20.5996 1.141 −18.9485 6.42738 0.5 −3.40979 1.25264 0.95 6.04566 20.1406 1.141 −19.2444 6.68026 0.5 −2.12565 2.31483 0.95 5.64973 19.6242 1.141 −19.4979 6.87949 0.5 −0.97853 3.49874 0.95 5.1853 19.0571 1.141 −19.723 7.00614 0.5 0.0458 4.75567 0.95 4.65143 18.4423 1.141 −19.9158 7.05043 0.5 0.95823 6.0525 0.95 4.04786 17.7835 1.141 −20.0569 7.03536 0.5 1.76974 7.363 0.95 3.37655 17.0836 1.141 −20.143 7.00293 0.5 2.49433 8.66389 0.95 2.64152 16.3442 1.141 −20.1975 6.97078 0.5 3.14457 9.93648 0.95 1.84995 15.5646 1.141 −20.3488 7.02937 0.6 3.72838 11.1671 0.95 1.00784 14.746 1.141 −20.4059 6.97441 0.6 4.25397 12.3435 0.95 0.11879 13.8927 1.141 −20.4671 6.87679 0.6 4.72918 13.4553 0.95 −0.81621 13.0128 1.141 −20.5035 6.70277 0.6 5.15873 14.4949 0.95 −1.80926 12.1294 1.141 −20.4696 6.45738 0.6 5.54629 15.4558 0.95 −2.88531 11.2859 1.141 −20.3629 6.15194 0.6 5.89471 16.3335 0.95 −4.0433 10.5025 1.141 −20.2084 5.77878 0.6 6.20598 17.1246 0.95 −5.28108 9.80367 1.141 −19.9962 5.33993 0.6 6.48164 17.8272 0.95 −6.58778 9.20587 1.141 −19.7243 4.83536 0.6 6.72239 18.4408 0.95 −7.94554 8.71258 1.141 −19.3917 4.26563 0.6 6.92911 18.9664 0.95 −9.33602 8.32205 1.141 −18.989 3.63759 0.6 7.10319 19.4059 0.95 −10.7414 8.02694 1.141 −18.504 2.96241 0.6 7.2431 19.7641 0.95 −12.1456 7.81691 1.141 −17.9271 2.25303 0.6 7.35921 20.0423 0.95 −13.535 7.68328 1.141 −17.2504 1.52429 0.6 7.42737 20.257 0.95 −14.8979 7.62225 1.141 −16.467 0.79441 0.6 7.40845 20.413 0.95 −16.2234 7.62464 1.141 −15.5707 0.08608 0.6 7.3505 20.4935 0.95 −17.5015 7.68713 1.141 −14.5568 −0.57221 0.6 7.28802 20.537 0.95 −18.7229 7.80481 1.141 −13.4231 −1.14361 0.6 7.23049 20.5583 0.95 −19.8794 7.97174 1.141 −12.1738 −1.5815 0.6 7.15087 20.5642 0.95 −20.9601 8.19861 1.141 −10.8257 −1.8327 0.6 7.03273 20.519 0.95 −21.9528 8.4912 1.141 −9.41432 −1.84954 0.6 6.91289 20.383 0.95 −22.8456 8.84743 1.141 −7.99062 −1.60759 0.6 6.79023 20.1736 0.95 −23.6456 9.22311 1.141 −6.60652 −1.11573 0.6 6.63431 19.9062 0.95 −24.3746 9.5609 1.141 −5.2994 −0.40964 0.6 6.44189 19.5779 0.95 −25.0467 9.82241 1.141 −4.08817 0.46535 0.6 6.21106 19.1862 0.95 −25.6623 9.98867 1.141 −2.98036 1.46854 0.6 5.94093 18.7295 0.95 −26.2119 10.0587 1.141 −1.97324 2.56206 0.6 5.62832 18.2086 0.95 −26.6826 10.0375 1.141 −1.05681 3.71215 0.6 5.27215 17.6243 0.95 −27.0628 9.94899 1.141 −0.22466 4.89525 0.6 4.87083 16.9787 0.95 −27.3492 9.82349 1.141 0.53018 6.09153 0.6 4.42255 16.2753 0.95 −27.5473 9.6889 1.141 1.21679 7.28287 0.6 3.92518 15.5188 0.95 −27.6717 9.57039 1.141 1.84356 8.45406 0.6 3.37591 14.7152 0.95 −27.7423 9.48427 1.141 2.41579 9.59326 0.6 2.77157 13.8723 0.95 −27.7854 9.42095 1.141

In the above table, the plane Z′=0 corresponds to the reference plane P0 situated at the base of the profile. This plane P0 is the intersection of the stacking axis AE of the set of vanes with the axisymmetric surface of the hub, i.e. it passes via the intersection between the axis AE and the surface 16A where it is assembled with the inner shroud 16. The plane Z′=1 corresponds to the reference plane P1 situated at the top of the profile. This plane P1 is the intersection between the axis AE and the axisymmetric surface of the casing, i.e. it passes via the intersection of the axis AE with the surface 12A where it is assembled with the outer ring 12.

By convention, the stacking axis AE of the set of vanes, for the vane of a nozzle, is the axis that extends in the radial direction Z and passes through the middle of the inter-vane throat. For a given vane, the inter-vane throat is the location where the distance between the trailing edge of the vane in question and the suction side of the preceding vane in the direction of rotation of the turbine is at a minimum.

This is the axis on which the various X,Y sections of the set of vanes are “stacked” when designing the set of vanes.

As mentioned at the beginning of the present description, the aerodynamic profile of the invention is substantially identical to the nominal profile defined in the above table, i.e. it departs from said nominal profile by very little at most, being defined in particular within an envelope of ±1 mm in a direction normal to the surface of the nominal profile, and/or having X,Y coordinates lying within a range of ±5% relative to the coordinates X,Y of the nominal profile.

The coordinates of the above table are given starting from a value Z′=0 in the reference plane P0.

The coordinate Z′ is non-dimensional, i.e. for a point P, situated at a distance D from the plane P0 (where D is measured along the axis Z), the value of Z′ is D/H, where H represents the total height of the profile as measured between the planes P0 and P1. Naturally, in the table above, by multiplying the coordinate Z′ by the height H, it is possible to obtain the complete coordinates of the vane.

By way of example, the total height H may lie in the range 90 centimeters (cm) to 130 cm, and is preferably about 108 cm. By way of example, the plane PO is situated at a distance of 250 cm to 350 cm, and is preferably about 319 cm from the axis A.

In the above table, the profile is characterized by fifteen sections at constant Z′ coordinates, for which the coordinates X and Y are specified. In each section plane at constant coordinate Z′, the section of the profile is given by a continuous and smooth curve, interconnecting all of the points (X,Y). In each section plane, the profile is interpolated so as to generate a uniform profile.

FIG. 3 is a diagram of a section of the profile 18 in a plane X,Y parallel to the plane P0. As stated above, the vane D2 is in particular a nozzle vane of the second stage of a turbine. This vane is therefore stationary in rotation. Arrow R shows the direction of rotation of the rotary wheel situated downstream from the nozzle of this second stage.

It is advantageous for the nozzle that includes the vane of the invention to have 102 to 122 vanes that present aerodynamic profiles as defined above. 

The invention claimed is
 1. An aerodynamic profile for a turbine vane, the profile being, when cold and in a non-coated state, substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Z′ given in Table 1, in which the coordinate Z′ is the quotient D/H, where D is the distance of the point under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane out to the end of the vane, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.
 2. The aerodynamic profile as claimed in claim 1, wherein said profile is defined within an envelope of ±1 mm in a direction normal to the surface of the nominal profile.
 3. The aerodynamic profile as claimed in claim 1, wherein the coordinates X,Y of said profile lie within a range of ±5% relative to the coordinates X,Y of the nominal profile.
 4. The aerodynamic profile as claimed in claim 1, wherein the vane is a nozzle vane forming a part of a stator of a turbine.
 5. The aerodynamic profile as claimed in claim 4, wherein the vane is a nozzle vane of the second stage of the turbine.
 6. The aerodynamic profile as claimed in claim 4, wherein the vane is a vane of the second stage nozzle of a turbine having four stages.
 7. A turbine vane, presenting an aerodynamic profile as claimed in claim
 1. 8. A turbine, including turbine vanes presenting aerodynamic profiles as claimed in claim
 1. 9. A turbine as claimed in claim 8, including a nozzle that is stationary in rotation, having 102 to 122 vanes.
 10. A turbine nozzle forming a portion of a turbine stator, wherein all the vanes of the nozzle present an aerodynamic profile as claimed in claim
 1. 11. A turbine nozzle as claimed in claim 10, including 102 to 122 vanes. 